verify sin(4x) tan(2x) = 1-cos(4x)

Question

am asked to verify each identity

Answer 1

Since tan(x/2)=(1-cos(x))/sin(x), then tan(2x)=(1-cos(4x))/sin(4x).

 

sin(4x)*tan(2x)=sin(4x)*(1-cos(4x))/sin(4x)=1-cos(4x)